There are of course cases where should and must have a noticeably different tone. I don't think you can make any general rule about them. "You should do it!" and "You must do it!" totally depend on the tone of the speaker.
"You must not enter the room", on the other hand, sounds like a clear command. "You should not enter the room" sounds like a warning or an advice. "Must" is used official speak when there is a clear line between what is allowed and what is not. But in everyday speak, it is not as clear.

I disagree with this statement. Young people may not believe in God but they know film stars and sports players cannot create miracles. When someone is injured or has a serious illness they pray to God. Before my father's operation, I gave him an amulet to protect him. I feel like people do not want to believe in God until they have something very serious happening.
How is that?

Through these experiences I gained generosity, flexibility, and perseverance. These traits are my strong points and allow me to enjoy and accept different cultures and values. I believe that these traits are indispensable qualities for a Japanese Language teacher who interacts with foreign students from various cultural backgrounds.

I think, like you said, 2 is officially correct.
There's a similar, but more common, phrase with the same structure:
'A growing number of people' with which you would always say 'seem to believe' even though number is singular. I'm not sure why.